Eric Chong
PHYS C1493
Partner: Albert Lee
Lab Date: November 30, 2006
Experiment 9: AC Circuits
Introduction
This lab makes widespread use of the digital oscilloscope in efforts to study the time and
frequencydependant behavior of an AC circuit, which is a circuit whose current is driven by a
voltage that varies with the passage of time.
With the AC circuit containing a resistance
R
,
capacitance
C
, and inductance
L
subject to varying frequencies of a sinusoidal voltage
V
, we
relate the voltage across the resistor
V
R
as a function of angular frequency
ω
to find the resonant
frequency and the full width at half maximum FWHM, using calculated graphs.
We also use the
oscilloscope to gauge the phase difference between the driving voltage and the voltage across the
resistor.
The experimental values for resonant frequency
ω
0
and phase difference
φ
can then be
compared to calculated values, given by the following equations:
0
1
LC
ϖ
=
,
1/
tan
L
C
R
φ

=
Procedure
Resonance
We begin this experiment by setting up the RLC circuit such that the inductor, capacitor, and a
decade resistor box are connected in series with a function generator and an oscilloscope.
Initially the decade resistor box is set to a resistance of
50 Ω
using a knob on the function
generator, and the function generator set to produce a sinusoidal signal in the range of
1 kHz
,
with a peaktopeak voltage of
V
pp
= 20 V
.
Making sure that CH 2 on the oscilloscope is
connected across the resistor, we vary the frequency on the function generator such that the wave
displayed on CH 2 peaks at some maximum value – the frequency at this peak value is the
resonance frequency,
ω
0
.
After recording this value, we scan over a wide range of frequencies
both above and below
ω
0
, taking into record
frequencies and their respective peakto
peak voltages as given by the oscilloscope.
We need a wide enough range such that we
can find and record the FWHM of the signal
– thus we record voltage amplitudes of at
least 20 points above and below
ω
0
.
This
procedure is repeated for resistances of
10
Ω
and
500 Ω.
We then replace the
150 mH
inductor in the RLC circuit with a large copper ring of
inductance
0.0225 H
, and using the function generator to sweep through a variety of frequencies,
we use the same method we used earlier to find the resonance frequency
ω
0
.
Using this value
along with the value of
C
, we can estimate the inductance
L
of the copper ring using the equation
given in the introduction.
Phase of Driving Voltage and V
R
We revert back to the
150 mH
inductor and eliminate the copper ring, while setting the resistance
to
30
Ω
– we should once again be able to see the driving voltage on CH 1 of the oscilloscope
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View Full Documentand the voltage across the resistor on CH 2.
In comparing the two sinusoidal curves, we proceed
in taking into account the relationship between the two when the frequency on the function
generator is varied above and below
ω
0
– we do this qualitatively by pointing out which curve
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 Spring '08
 LAB
 Physics, Alternating Current, Frequency, RLC, decade resistor box

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